Does the Free Market fix the problem of food deserts in low income communities?

I got into an argument with a friend of mine a while back(he’s my roommate in college) about the issue of food deserts. I told him that low income(often minority and especially black) communities have to deal with food deserts(wherein poor communities are faced with a lack of grocery stores serving fresher produce and healthier products), but he disagreed. He stated that the Free Market would fix the problem naturally, as businesses would would see a demand for a service(specifically grocery stores serving fresh produce and healthy goods) and would come in and naturally fix the problem. We ended up being stuck at an impasse for a while, and thus the nature of my question.

Specifically I want to know if the free market itself fixes these problems naturally and makes further government incentives are unnecessary. What do you all think?